Of course uilleann pipes and Scottish pipes are completely different animals and it (to me) doesn't make sense to discuss them together.
For uilleann pipes the quiet way to go is with a 'flat' chanter, down in B perhaps. A narrow-bore B chanter with a soft reed is going to put out much less volume than a big-bore strongly-reeded D chanter.
For Scottish pipes, SSPs can be very quiet, often too quiet. Usually the problem is to get them loud enough.
I've never cared for the John Walsh 'shuttlepipes'. (Keeping in mind that 'shuttlepipe' isn't a type of bagpipe so much as it is John Walsh's brand name for his SSP with shuttle drone.)
What work far better are John Walsh's 'Smallpipes in A 2000.' All the reeds are plastic, and the set comes from John perfectly 'set up' and voiced. It can't be beat for a low cost extremely reliable good-sounding set of SSPs.
Here's a video of somebody playing one
http://www.youtube.com/watch?v=PBgUUYhMXSIMost people coming from Highland pipes wildly overblow SSPs and it takes a while for them to get used to the lower pressure.